Evaluation of RISK survival models

This document highlights the use of

for the evaluation (RRPlot), and calibration of cox models (CoxRiskCalibration) or logistic models (CalibrationProbPoissonRisk) of survival data.

Furthermore, it can be used to evaluate any Risk index that reruns the probability of a future event on external data-set.

This document will use the survival::rotterdam, and survival::gbsg data-sets to train and predict the risk of cancer recurrence after surgery. Both Cox and Logistic models will be trained and evaluated.

Here are some sample plots returned by the evaluated functions:

The libraries

library(survival)
library(FRESA.CAD)
## Loading required package: Rcpp
## Loading required package: stringr
## Loading required package: miscTools
## Loading required package: Hmisc
## 
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
## 
##     format.pval, units
## Loading required package: pROC
## Type 'citation("pROC")' for a citation.
## 
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
## 
##     cov, smooth, var
source("~/GitHub/FRESA.CAD/R/RRPlot.R")
source("~/GitHub/FRESA.CAD/R/PoissonEventRiskCalibration.R")
op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

Breast Cancer Royston-Altman data

data(gbsg, package=“survival”) and data(rotterdam, package=“survival”)

gbsgdata <- gbsg
rownames(gbsgdata) <- gbsgdata$pid
gbsgdata$pid <- NULL

odata <-rotterdam
rownames(odata) <- odata$pid
odata$pid <- NULL
odata$rfstime <- odata$rtime
odata$status <- odata$recur
odata$rtime <- NULL
odata$recur <- NULL

odata <- odata[,colnames(odata) %in% colnames(gbsgdata)]

odata$size <- 10*(odata$size=="<=20") + 
  35*(odata$size=="20-50") + 
  60*(odata$size==">50")

data <- as.data.frame(model.matrix(Surv(rfstime,status)~.*.,odata))

data$`(Intercept)` <- NULL

dataBrestCancerTrain <- cbind(time=odata[rownames(data),"rfstime"],status=odata[rownames(data),"status"],data)

colnames(dataBrestCancerTrain) <-str_replace_all(colnames(dataBrestCancerTrain),":","_")
colnames(dataBrestCancerTrain) <-str_replace_all(colnames(dataBrestCancerTrain)," ","")
colnames(dataBrestCancerTrain) <-str_replace_all(colnames(dataBrestCancerTrain),"\\.","_")
colnames(dataBrestCancerTrain) <-str_replace_all(colnames(dataBrestCancerTrain),"-","_")
colnames(dataBrestCancerTrain) <-str_replace_all(colnames(dataBrestCancerTrain),">","_")
dataBrestCancerTrain$time <- dataBrestCancerTrain$time/365 ## To years


pander::pander(table(odata[rownames(data),"status"]),caption="rotterdam")
rotterdam
0 1
1464 1518

data(gbsg, package=“survival”) data conditioning

gbsgdata <- gbsgdata[,colnames(odata)]
data <- as.data.frame(model.matrix(Surv(rfstime,status)~.*.,gbsgdata))

data$`(Intercept)` <- NULL

dataBrestCancerTest <- cbind(time=gbsgdata[rownames(data),"rfstime"],status=gbsgdata[rownames(data),"status"],data)

colnames(dataBrestCancerTest) <-str_replace_all(colnames(dataBrestCancerTest),":","_")
colnames(dataBrestCancerTest) <-str_replace_all(colnames(dataBrestCancerTest)," ","")
colnames(dataBrestCancerTest) <-str_replace_all(colnames(dataBrestCancerTest),"\\.","_")
colnames(dataBrestCancerTest) <-str_replace_all(colnames(dataBrestCancerTest),"-","_")
colnames(dataBrestCancerTest) <-str_replace_all(colnames(dataBrestCancerTest),">","_")
dataBrestCancerTest$time <- dataBrestCancerTest$time/365

pander::pander(table(odata[rownames(data),"status"]), caption="gbsg")
gbsg
0 1
499 183

Cox Modeling

ml <- BSWiMS.model(Surv(time,status)~.,data=dataBrestCancerTrain,loops=1,NumberofRepeats = 5)

—–.

sm <- summary(ml)
pander::pander(sm$coefficients)
  Estimate lower HR upper u.Accuracy r.Accuracy full.Accuracy u.AUC r.AUC full.AUC IDI NRI z.IDI z.NRI Delta.AUC Frequency
age_nodes 0.000716 1.001 1.001 1.001 0.626 0.600 0.632 0.630 0.601 0.634 0.03040 0.4594 12.81 14.37 0.033056 1
size_grade 0.005649 1.005 1.006 1.006 0.598 0.623 0.632 0.599 0.626 0.634 0.01868 0.3914 9.82 11.29 0.007947 1
nodes 0.086582 1.082 1.090 1.099 0.637 0.642 0.643 0.640 0.643 0.644 0.00745 0.0564 8.33 1.66 0.000148 1
size 0.006888 1.005 1.007 1.009 0.595 0.641 0.643 0.595 0.642 0.644 0.01447 0.3587 8.05 9.97 0.001322 1
size_nodes -0.000378 1.000 1.000 1.000 0.624 0.643 0.643 0.629 0.644 0.644 0.00346 0.3430 7.25 9.57 -0.000377 1
age_size -0.000149 1.000 1.000 1.000 0.567 0.627 0.632 0.568 0.630 0.634 0.00635 0.1935 5.95 5.36 0.004078 1
grade 0.204934 1.146 1.227 1.314 0.565 0.637 0.643 0.561 0.638 0.644 0.00926 0.2069 5.88 6.31 0.005344 1
age -0.003113 0.996 0.997 0.998 0.513 0.628 0.643 0.513 0.628 0.644 0.00416 0.0917 5.27 2.51 0.015465 1
grade_nodes -0.013784 0.981 0.986 0.992 0.635 0.645 0.643 0.639 0.646 0.644 0.00207 -0.0910 5.03 -2.55 -0.002609 1

Cox Model Performance

Here we evaluate the model using the RRPlot() function.

The evaluation of the raw Cox model with RRPlot()

Here we will use the predicted event probability assuming a baseline hazard for events withing 5 years

timeinterval <- 5 # Five years

h0 <- sum(dataBrestCancerTrain$status & dataBrestCancerTrain$time <= timeinterval)
h0 <- h0/sum((dataBrestCancerTrain$time > timeinterval) | (dataBrestCancerTrain$status==1))

pander::pander(t(c(h0=h0,timeinterval=timeinterval)),caption="Initial Parameters")
Initial Parameters
h0 timeinterval
0.429 5 
index <- predict(ml,dataBrestCancerTrain)
rdata <- cbind(dataBrestCancerTrain$status,ppoisGzero(index,h0))

rrAnalysisTrain <- RRPlot(rdata,atProb=c(0.90,0.80),
                     timetoEvent=dataBrestCancerTrain$time,
                     title="Train: Breast Cancer",
                     ysurvlim=c(0.00,1.0),
                     riskTimeInterval=timeinterval)

ROC: Train: Breast Cancer

As we can see the Observed probability as well as the Time vs. Events are not calibrated.

Uncalibrated Performance Report

pander::pander(t(rrAnalysisTrain$OERatio),caption="O/E Ratio")
O/E Ratio
est lower upper
1.13 1.07 1.19 
pander::pander(t(rrAnalysisTrain$OE95ci),caption="O/E Ratio")
O/E Ratio
mean 50% 2.5% 97.5%
1.13 1.13 1.12 1.14 
pander::pander(t(rrAnalysisTrain$OAcum95ci),caption="O/Acum Ratio")
O/Acum Ratio
mean 50% 2.5% 97.5%
1.34 1.34 1.34 1.34 
pander::pander(rrAnalysisTrain$c.index$cstatCI,caption="C. Index")
mean.C Index median lower upper
0.676 0.676 0.662 0.69 
pander::pander(t(rrAnalysisTrain$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.694 0.675 0.713 
pander::pander((rrAnalysisTrain$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.299 0.276 0.323 
pander::pander((rrAnalysisTrain$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.9 0.883 0.915 
pander::pander(t(rrAnalysisTrain$thr_atP),caption="Probability Thresholds")
Probability Thresholds
90% 80%
0.459 0.389 
pander::pander(t(rrAnalysisTrain$RR_atP),caption="Risk Ratio")
Risk Ratio
est lower upper
1.69 1.59 1.8 
pander::pander(rrAnalysisTrain$sufdif,caption="Logrank test")
Logrank test Chisq = 465.079317 on 2 degrees of freedom, p = 0.000000
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 1985 816 1144 93.9 385.7
class=1 396 248 177 28.0 31.8
class=2 601 454 197 336.3 391.3

Cox Calibration

op <- par(no.readonly = TRUE)


calprob <- CoxRiskCalibration(ml,dataBrestCancerTrain,"status","time")


pander::pander(c(h0=calprob$h0,
                 Gain=calprob$hazardGain,
                 DeltaTime=calprob$timeInterval),
               caption="Cox Calibration Parameters")
h0 Gain DeltaTime
0.698 1.35 6.97

The RRplot() of the calibrated model

h0 <- calprob$h0
timeinterval <- calprob$timeInterval;

rdata <- cbind(dataBrestCancerTrain$status,calprob$prob)


rrAnalysisTrain <- RRPlot(rdata,atProb=c(0.90,0.80),
                     timetoEvent=dataBrestCancerTrain$time,
                     title="Cal. Train: Breast Cancer",
                     ysurvlim=c(0.00,1.0),
                     riskTimeInterval=timeinterval)

ROC: Cal. Train: Breast Cancer

Calibrated Train Performance

pander::pander(t(rrAnalysisTrain$OERatio),caption="O/E Ratio")
O/E Ratio
est lower upper
0.998 0.949 1.05 
pander::pander(t(rrAnalysisTrain$OE95ci),caption="O/E Ratio")
O/E Ratio
mean 50% 2.5% 97.5%
0.977 0.977 0.969 0.985 
pander::pander(t(rrAnalysisTrain$OAcum95ci),caption="O/Acum Ratio")
O/Acum Ratio
mean 50% 2.5% 97.5%
1.01 1.01 1.01 1.01 
pander::pander(rrAnalysisTrain$c.index$cstatCI,caption="C. Index")
mean.C Index median lower upper
0.676 0.677 0.663 0.69 
pander::pander(t(rrAnalysisTrain$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.694 0.675 0.713 
pander::pander((rrAnalysisTrain$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.299 0.276 0.323 
pander::pander((rrAnalysisTrain$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.9 0.883 0.915 
pander::pander(t(rrAnalysisTrain$thr_atP),caption="Probability Thresholds")
Probability Thresholds
90% 80%
0.632 0.551 
pander::pander(t(rrAnalysisTrain$RR_atP),caption="Risk Ratio")
Risk Ratio
est lower upper
1.69 1.59 1.8 
pander::pander(rrAnalysisTrain$sufdif,caption="Logrank test")
Logrank test Chisq = 465.079317 on 2 degrees of freedom, p = 0.000000
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 1985 816 1144 93.9 385.7
class=1 396 248 177 28.0 31.8
class=2 601 454 197 336.3 391.3

Performance on the external data set

index <- predict(ml,dataBrestCancerTest)
pp <- predictionStats_binary(cbind(dataBrestCancerTest$status,index),plotname="Breast Cancer")

Breast Cancer 

par(op)


prob <- ppoisGzero(index,h0)
rdata <- cbind(dataBrestCancerTest$status,prob)
rrCoxTestAnalysis <- RRPlot(rdata,atThr=rrAnalysisTrain$thr_atP,
                     timetoEvent=dataBrestCancerTest$time,
                     title="Test: Breast Cancer",
                     ysurvlim=c(0.00,1.0),
                     riskTimeInterval=timeinterval)

ROC: Test: Breast Cancer 

par(op)

External Data Report

pander::pander(t(rrCoxTestAnalysis$OERatio),caption="O/E Ratio")
O/E Ratio
est lower upper
1.33 1.19 1.49 
pander::pander(rrCoxTestAnalysis$c.index,caption="C. Index")

  • C Index: 0.664

  • Dxy: 0.328

  • S.D.: 0.0311

  • n: 686

  • missing: 0

  • uncensored: 299

  • Relevant Pairs: 266144

  • Concordant: 176737

  • Uncertain: 203702

  • cstatCI:

    mean.C Index median lower upper
    0.664 0.664 0.634 0.693 
pander::pander(t(rrCoxTestAnalysis$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.66 0.619 0.7 
pander::pander((rrCoxTestAnalysis$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.328 0.275 0.384 
pander::pander((rrCoxTestAnalysis$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.873 0.836 0.905 
pander::pander(t(rrCoxTestAnalysis$thr_atP),caption="Probability Thresholds")
Probability Thresholds
90% 80%
0.632 0.551 
pander::pander(t(rrCoxTestAnalysis$RR_atP),caption="Risk Ratio")
Risk Ratio
est lower upper
1.79 1.53 2.09 
pander::pander(rrCoxTestAnalysis$sufdif,caption="Logrank test")
Logrank test Chisq = 81.471750 on 2 degrees of freedom, p = 0.000000
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 457 164 221.4 14.888 58.181
class=1 82 37 33.2 0.438 0.494
class=2 147 98 44.4 64.710 77.254

Calibrating the index on the test data

calprob <- CoxRiskCalibration(ml,dataBrestCancerTest,"status","time")

pander::pander(c(h0=calprob$h0,
                 Gain=calprob$hazardGain,
                 DeltaTime=calprob$timeInterval),
               caption="Cox Calibration Parameters")
h0 Gain DeltaTime
0.535 0.925 4.87 
rdata <- cbind(dataBrestCancerTest$status,calprob$prob)

rrAnalysis <- RRPlot(rdata,atProb=c(0.90,0.80),
                     timetoEvent=dataBrestCancerTest$time,
                     title="Cal. Test: Breast Cancer",
                     ysurvlim=c(0.00,1.0),
                     riskTimeInterval=calprob$timeInterval)

ROC: Cal. Test: Breast Cancer

After Calibration Report

pander::pander(t(rrAnalysis$OERatio),caption="O/E Ratio")
O/E Ratio
est lower upper
1.23 1.09 1.37 
pander::pander(rrAnalysis$c.index,caption="C. Index")

  • C Index: 0.664

  • Dxy: 0.328

  • S.D.: 0.0311

  • n: 686

  • missing: 0

  • uncensored: 299

  • Relevant Pairs: 266144

  • Concordant: 176737

  • Uncertain: 203702

  • cstatCI:

    mean.C Index median lower upper
    0.664 0.664 0.634 0.697 
pander::pander(t(rrAnalysis$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.66 0.619 0.7 
pander::pander((rrAnalysis$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.264 0.215 0.318 
pander::pander((rrAnalysis$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.899 0.865 0.927 
pander::pander(t(rrAnalysis$thr_atP),caption="Probability Thresholds")
Probability Thresholds
90% 80%
0.585 0.484 
pander::pander(t(rrAnalysis$RR_atP),caption="Risk Ratio")
Risk Ratio
est lower upper
1.74 1.48 2.05 
pander::pander(rrAnalysis$sufdif,caption="Logrank test")
Logrank test Chisq = 80.835092 on 2 degrees of freedom, p = 0.000000
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 482 173 232.4 15.20 69.5
class=1 86 47 32.0 7.02 7.9
class=2 118 79 34.6 57.14 65.4

Logistic Model

Here we train a logistic model on the same data set

## Only label subjects that present event withing five years

dataBrestCancerR <- subset(dataBrestCancerTrain, time>=5 | status==1)
dataBrestCancerR$status <- dataBrestCancerR$status * (dataBrestCancerR$time < 5)
dataBrestCancerR$time <- NULL

#ml <- BSWiMS.model(status~1,data=dataBrestCancerR,loops=20,NumberofRepeats = 5)
mlog <- BSWiMS.model(status~1,data=dataBrestCancerR,loops=1,NumberofRepeats = 5)

—–..

sm <- summary(mlog)
pander::pander(sm$coefficients)
  Estimate lower OR upper u.Accuracy r.Accuracy full.Accuracy u.AUC r.AUC full.AUC IDI NRI z.IDI z.NRI Delta.AUC Frequency
size_nodes 1.05e-03 1.001 1.001 1.001 0.669 0.571 0.668 0.627 0.500 0.628 0.11233 0.63654 17.86 18.870 0.128490 1
nodes 4.33e-02 1.040 1.044 1.048 0.676 0.634 0.690 0.639 0.621 0.662 0.07110 0.57106 14.13 16.179 0.040494 1
grade_nodes 1.50e-02 1.014 1.015 1.016 0.682 0.637 0.686 0.649 0.624 0.655 0.06580 0.54866 13.66 15.650 0.031087 1
age_nodes 1.06e-03 1.001 1.001 1.001 0.678 0.653 0.686 0.642 0.621 0.657 0.03346 0.21312 9.39 5.710 0.035896 1
size_grade 1.75e-03 1.001 1.002 1.002 0.632 0.682 0.686 0.626 0.646 0.655 0.01787 0.29411 6.74 7.728 0.008648 1
age_size 8.73e-05 1.000 1.000 1.000 0.608 0.682 0.686 0.577 0.649 0.657 0.01534 0.29152 6.41 7.652 0.007600 1
grade 2.27e-01 1.168 1.254 1.347 0.571 0.683 0.690 0.500 0.653 0.662 0.01340 0.19036 6.20 4.983 0.008461 1
age_meno -6.04e-03 0.992 0.994 0.996 0.571 0.676 0.686 0.500 0.645 0.657 0.00782 0.08057 4.76 2.337 0.012065 1
age_pgr -5.42e-06 1.000 1.000 1.000 0.571 0.686 0.686 0.500 0.656 0.657 0.00512 0.00745 4.11 0.194 0.000417 1
age_grade -1.65e-03 0.997 0.998 0.999 0.574 0.690 0.690 0.507 0.661 0.662 0.00454 0.11372 3.60 2.960 0.000315 1
meno_grade 1.02e-01 1.045 1.107 1.173 0.571 0.683 0.686 0.500 0.652 0.657 0.00425 0.20428 3.47 5.343 0.004441 1
nodes_hormon -1.38e-02 0.979 0.986 0.994 0.587 0.688 0.686 0.526 0.658 0.655 0.00280 0.45522 3.44 12.150 -0.002853 1
size 3.94e-03 1.002 1.004 1.006 0.611 0.693 0.690 0.618 0.663 0.662 0.00507 0.21050 3.42 5.600 -0.001075 1
meno_pgr 3.19e-04 1.000 1.000 1.001 0.571 0.687 0.686 0.500 0.657 0.657 0.00316 0.05977 3.35 1.558 -0.000429 1
pgr -1.07e-04 1.000 1.000 1.000 0.571 0.689 0.686 0.500 0.659 0.655 0.00257 0.19759 2.64 5.745 -0.004123 1
meno_nodes -2.60e-02 0.955 0.974 0.994 0.640 0.686 0.686 0.595 0.656 0.657 0.00264 -0.06329 2.59 -1.645 0.000631 1
grade_pgr -3.51e-05 1.000 1.000 1.000 0.571 0.669 0.668 0.500 0.627 0.628 0.00241 0.17471 2.55 5.058 0.001252 1
meno_size 2.34e-03 1.000 1.002 1.004 0.604 0.691 0.690 0.578 0.663 0.662 0.00185 0.10227 2.43 2.662 -0.001378 1

Logistic Model Performance

op <- par(no.readonly = TRUE)


cprob <- predict(mlog,dataBrestCancerTrain)

rdata <- cbind(dataBrestCancerTrain$status,cprob)
rrAnalysisTrain <- RRPlot(rdata,atProb=c(0.90,0.80),
                     timetoEvent=dataBrestCancerTrain$time,
                     title="Logistic Train: Breast Cancer",
                     ysurvlim=c(0.00,1.0),
                     riskTimeInterval=5.0)

ROC: Logistic Train: Breast Cancer 

par(op)

Training Report

pander::pander(t(rrAnalysisTrain$OERatio),caption="O/E Ratio")
O/E Ratio
est lower upper
0.957 0.91 1.01 
pander::pander(rrAnalysisTrain$c.index,caption="C. Index")

  • C Index: 0.68

  • Dxy: 0.36

  • S.D.: 0.014

  • n: 2982

  • missing: 0

  • uncensored: 1518

  • Relevant Pairs: 6184528

  • Concordant: 4206588

  • Uncertain: 2703838

  • cstatCI:

    mean.C Index median lower upper
    0.68 0.681 0.667 0.695 
pander::pander(t(rrAnalysisTrain$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.695 0.677 0.714 
pander::pander((rrAnalysisTrain$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.327 0.303 0.351 
pander::pander((rrAnalysisTrain$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.9 0.883 0.915 
pander::pander(t(rrAnalysisTrain$thr_atP),caption="Probability Thresholds")
Probability Thresholds
90% 80%
0.542 0.431 
pander::pander(t(rrAnalysisTrain$RR_atP),caption="Risk Ratio")
Risk Ratio
est lower upper
1.77 1.66 1.88 
pander::pander(rrAnalysisTrain$sufdif,caption="Logrank test")
Logrank test Chisq = 543.347175 on 2 degrees of freedom, p = 0.000000
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 1975 804 1145 101.5 418.9
class=1 364 218 169 14.1 15.9
class=2 643 496 204 418.2 490.7

Results on the validation set using Logistic model

pre <- predict(mlog,dataBrestCancerTest)
rdata <- cbind(dataBrestCancerTest$status,pre)

rrAnalysis <- RRPlot(rdata,atThr=rrAnalysisTrain$thr_atP,
                     timetoEvent=dataBrestCancerTest$time,
                     title="Logistic Test: Breast Cancer",
                     ysurvlim=c(0.00,1.0),
                     riskTimeInterval=5)

ROC: Logistic Test: Breast Cancer 

par(op)

Validation Report

pander::pander(t(rrAnalysis$OERatio),caption="O/E Ratio")
O/E Ratio
est lower upper
1.13 1 1.26 
pander::pander(rrAnalysis$c.index,caption="C. Index")

  • C Index: 0.669

  • Dxy: 0.338

  • S.D.: 0.0309

  • n: 686

  • missing: 0

  • uncensored: 299

  • Relevant Pairs: 266144

  • Concordant: 178115

  • Uncertain: 203702

  • cstatCI:

    mean.C Index median lower upper
    0.669 0.669 0.639 0.698 
pander::pander(t(rrAnalysis$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.669 0.628 0.709 
pander::pander((rrAnalysis$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.395 0.339 0.453 
pander::pander((rrAnalysis$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.832 0.791 0.868 
pander::pander(t(rrAnalysis$thr_atP),caption="Probability Thresholds")
Probability Thresholds
90% 80%
0.542 0.431 
pander::pander(t(rrAnalysis$RR_atP),caption="Risk Ratio")
Risk Ratio
est lower upper
1.8 1.54 2.11 
pander::pander(rrAnalysis$sufdif,caption="Logrank test")
Logrank test Chisq = 92.507991 on 2 degrees of freedom, p = 0.000000
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 369 121 181.7 20.2997 52.3868
class=1 134 60 61.7 0.0479 0.0604
class=2 183 118 55.5 70.2342 88.0195

Logistic Model Poisson Calibration

riskdata <- cbind(dataBrestCancerTrain$status,predict(mlog,dataBrestCancerTrain,type="prob"),dataBrestCancerTrain$time)
calprob <- CalibrationProbPoissonRisk(riskdata)

pander::pander(c(h0=calprob$h0,
                 Gain=calprob$hazardGain,
                 DeltaTime=calprob$timeInterval),
               caption="Logistic Calibration Parameters")
h0 Gain DeltaTime
0.676 1.31 7.14 
timeinterval <- calprob$timeInterval;
gain <- calprob$hazardGain

rdata <- cbind(dataBrestCancerTrain$status,calprob$prob)


rrAnalysisTrain <- RRPlot(rdata,atProb=c(0.90,0.80),
                     timetoEvent=dataBrestCancerTrain$time,
                     title="Cal. Logistic Train: Breast Cancer",
                     ysurvlim=c(0.00,1.0),
                     riskTimeInterval=timeinterval)

ROC: Cal. Logistic Train: Breast Cancer 

par(op)

Report of the calibrated logistic: training

pander::pander(t(rrAnalysisTrain$OERatio),caption="O/E Ratio")
O/E Ratio
est lower upper
1.02 0.974 1.08 
pander::pander(rrAnalysisTrain$c.index,caption="C. Index")

  • C Index: 0.68

  • Dxy: 0.36

  • S.D.: 0.014

  • n: 2982

  • missing: 0

  • uncensored: 1518

  • Relevant Pairs: 6184528

  • Concordant: 4206588

  • Uncertain: 2703838

  • cstatCI:

    mean.C Index median lower upper
    0.68 0.68 0.668 0.694 
pander::pander(t(rrAnalysisTrain$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.695 0.677 0.714 
pander::pander((rrAnalysisTrain$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.327 0.303 0.351 
pander::pander((rrAnalysisTrain$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.9 0.883 0.915 
pander::pander(t(rrAnalysisTrain$thr_atP),caption="Probability Thresholds")
Probability Thresholds
90% 80%
0.639 0.521 
pander::pander(t(rrAnalysisTrain$RR_atP),caption="Risk Ratio")
Risk Ratio
est lower upper
1.77 1.66 1.88 
pander::pander(rrAnalysisTrain$sufdif,caption="Logrank test")
Logrank test Chisq = 543.347175 on 2 degrees of freedom, p = 0.000000
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 1975 804 1145 101.5 418.9
class=1 364 218 169 14.1 15.9
class=2 643 496 204 418.2 490.7 
probLog <- predict(mlog,dataBrestCancerTest)
aprob <- adjustProb(probLog,gain)

rdata <- cbind(dataBrestCancerTest$status,aprob)
rrAnalysisTestLogistic <- RRPlot(rdata,atThr=rrAnalysisTrain$thr_atP,
                     timetoEvent=dataBrestCancerTest$time,
                     title="Cal. Logistic Test: Breast Cancer",
                     ysurvlim=c(0.00,1.0),
                     riskTimeInterval=timeinterval)

ROC: Cal. Logistic Test: Breast Cancer 

par(op)

Report of the calibrated validation

pander::pander(t(rrAnalysisTestLogistic$OERatio),caption="O/E Ratio")
O/E Ratio
est lower upper
1.22 1.08 1.36 
pander::pander(rrAnalysisTestLogistic$c.index,caption="C. Index")

  • C Index: 0.669

  • Dxy: 0.338

  • S.D.: 0.0309

  • n: 686

  • missing: 0

  • uncensored: 299

  • Relevant Pairs: 266144

  • Concordant: 178115

  • Uncertain: 203702

  • cstatCI:

    mean.C Index median lower upper
    0.669 0.669 0.636 0.699 
pander::pander(t(rrAnalysisTestLogistic$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.669 0.628 0.709 
pander::pander((rrAnalysisTestLogistic$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.395 0.339 0.453 
pander::pander((rrAnalysisTestLogistic$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.832 0.791 0.868 
pander::pander(t(rrAnalysisTestLogistic$thr_atP),caption="Probability Thresholds")
Probability Thresholds
90% 80%
0.639 0.521 
pander::pander(t(rrAnalysisTestLogistic$RR_atP),caption="Risk Ratio")
Risk Ratio
est lower upper
1.8 1.54 2.11 
pander::pander(rrAnalysisTestLogistic$sufdif,caption="Logrank test")
Logrank test Chisq = 92.507991 on 2 degrees of freedom, p = 0.000000
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 369 121 181.7 20.2997 52.3868
class=1 134 60 61.7 0.0479 0.0604
class=2 183 118 55.5 70.2342 88.0195

Comparing the COX and Logistic Models on the Independent Data

pander::pander(t(rrCoxTestAnalysis$OAcum95ci))
mean 50% 2.5% 97.5%
0.841 0.841 0.839 0.842 
pander::pander(t(rrAnalysisTestLogistic$OAcum95ci))
mean 50% 2.5% 97.5%
0.791 0.791 0.791 0.792 
pander::pander(t(rrCoxTestAnalysis$OE95ci))
mean 50% 2.5% 97.5%
1.07 1.07 1.03 1.1 
pander::pander(t(rrAnalysisTestLogistic$OE95ci))
mean 50% 2.5% 97.5%
0.955 0.956 0.923 0.984 
maxobs <- sum(dataBrestCancerTest$status)

par(mfrow=c(1,2),cex=0.75)

plot(rrCoxTestAnalysis$CumulativeOvs,type="l",lty=1,
     main="Cumulative Probability",
     xlab="Observed",
     ylab="Cumulative Probability",
     ylim=c(0,maxobs),
     xlim=c(0,maxobs))
lines(rrAnalysisTestLogistic$CumulativeOvs,lty=2,col="red")
lines(x=c(0,maxobs),y=c(0,maxobs),lty=3,col="gray")
legend("topleft",legend = c("Cox","Logistic","Ideal"),
       col=c("black","red","gray"),
       lty=c(1,2,3),
       cex=0.75
)


plot(rrCoxTestAnalysis$CumulativeOvs$Observed,
     rrCoxTestAnalysis$CumulativeOvs$Cumulative-
       rrCoxTestAnalysis$CumulativeOvs$Observed,
     main="Cumulative Risk Difference",
     xlab="Observed",
     ylab="Cumulative Risk - Observed",
     type="l",
     lty=1)
lines(rrAnalysisTestLogistic$CumulativeOvs$Observed,
     rrAnalysisTestLogistic$CumulativeOvs$Cumulative-
       rrAnalysisTestLogistic$CumulativeOvs$Observed,
     lty=2,
     col="red")
legend("topleft",legend = c("Cox","Logistic"),
       col=c("black","red"),
       lty=c(1,2),
       cex=0.75
)

plot(rrCoxTestAnalysis$OEData[,2:3],type="l",lty=1,
     main="Expected over Time",
     xlab="Observed",
     ylab="Expected",
     ylim=c(0,maxobs),
     xlim=c(0,maxobs))
lines(rrAnalysisTestLogistic$OEData[,2:3],lty=2,col="red")
lines(x=c(0,maxobs),y=c(0,maxobs),lty=3,col="gray")
legend("topleft",legend = c("Cox","Logistic","Ideal"),
       col=c("black","red","gray"),
       lty=c(1,2,3),
       cex=0.75
)

plot(rrCoxTestAnalysis$OEData$Observed,
     rrCoxTestAnalysis$OEData$Expected-
       rrCoxTestAnalysis$OEData$Observed,
     main="Expected vs Observed Difference",
     xlab="Observed",
     ylab="Cumulative - Observed",
     type="l",
     lty=1)
lines(rrAnalysisTestLogistic$OEData$Observed,
     rrAnalysisTestLogistic$OEData$Expected-
       rrAnalysisTestLogistic$OEData$Observed,
     lty=2,col="red")

legend("bottomleft",legend = c("Cox","Logistic"),
       col=c("black","red"),
       lty=c(1,2),
       cex=0.75
)

par(op)